ELECTRIC AND MAGNETIC INDUCTIONS IN THE SURROUNDING FIELD. 285 
Since C tubes move in through the inner circle per second, 
KE rdr 
9 
tubes move in 
m 
KE rdr 
2C 
of a second, i.e., all the tubes passing through the band will have just moved 
KE rdr 
2C ’ 
in in this time. The outermost tubes therefore describe the space dr in time 
2C 
or the velocity is r—-. Now we know that if It be the resistance per unit length 
E 
C = —. Hence we may put the velocity in the form 
Ja 
2 1 
krV 
which is independent of the current. 
To take a special case let us calculate the velocity just outside the boundary of a 
copper wire, the specific resistance of copper being 1642 in electromagnetic measure. 
Then if a be the radius of the wire 
1642 
R= 
TTCr 
and K=— where v is the ratio of the units, which in air may be taken as 3 X 10 10 . 
Then the velocity 
2v 2 7TO 2 
1642a 
2 x 9 x HPtto 
1642 
= 345 X 10 16 a 
At greater distances the velocity will be less, diminishing according to the inverse 
distance. 
The hypothetical velocity of propagation of the magnetic induction may be calcu- 
lated in a similar manner. The intensity at a distance r from the axis is — and the 
induction is ~~~ The area of each tube is therefore and the number lying in a 
ring of rectangular section with depth unity and internal and external radii r and 
r-\-dr, will be 1 X dr- 
r 2fjbQ>dr 
2/^C dr 
2/jlC r 
But E tubes move in per second through the inner face of the ring, so that 
tubes move in in time or this is the time taken by the outermost tubes to move 
E?’ J 
across the ring describing a distance dr. The velocity is therefore 
Er_ Hr 
2^C~2/x 
which is again independent of the current. 
mdccclxxxv. 2 p 
